Answer:
x = -4 or x = -1
Step-by-step explanation:
Given equation is :
10x+6 = -2x²-2
Adding 2x² and 2 to both sides of above equation , we get
2x²+2 +10x+6 = -2x²-2 +2x²+2
Adding like terms , we get
2x²+10x+8 = 0
As we have noticed that there are multiples of 2.
Taking 2 as common,we get
2(x²+5x+4) = 0
Multiplying by 1/2 to both sides of above equation , we get
1/2.2(x²+5x+4) = 1/2.0
x²+5x+4 = 0
Split the middle term of above equation so that the sum of two term should be 5 and their product be 4.
x²+4x+x+4 = 0
Making two groups ,we get
x(x+4)+1(x+4)
Taking (x+4) common,we get
(x+4)(x+1) = 0
Applying Zero-Product Property to above equation, we get
x+4 = 0 or x+1 = 0
Firstly, solve x+4 = 0
Adding -4 to both sides of above equation,we get
x+4-4 = 0-4
x +0 = -4
x = -4
Secondly, solve x+1 = 0
Adding -1 to both sides of above equation,we get
x+1-1 = 0-1
x = -1
Hence, the solution of 10x+6 = -2x²-2 is {-4,-1}.
